text:
Angle of attack difference between outer wing and inner wing during a descending turn and climbing turn
I understand that during an ascending or descending turn the angles of attack of the inner wing and outer wing are different.
However, I don't understand why then ascending and turning, the outer wing has greater AOA than the inner wing but during descending and turning, the inner wing has greater AOA than the outer wing.
Clarification:
My confusion is that, for example, if the AOA is greater for the outer wing, then the AOA should always be greater for the outer wing regardless the airplane is climbing or descending.

Do you know what (velocity) components determine the angle of attack?
How do these components differ between the inner wing and outer wing?
How do these components differ for ascending and descending?

Really the question should not say that the difference in angle-of-attack is "because they travel at different speeds"-- that implies that the effect should be present in a constant-altitude turn which is not accurate.  The question could be improved by deleting the entire first paragraph.

What do you mean exactly by "ascending or descending turn"?

@MikeY surely that needs no clarification-- a positive vertical speed or a negative vertical speed.

It's not clear to me that the assertion "..ascending and turning, the outer wing has greater AOA...during descending and turning, the inner wing has greater AOA" is a true statement.

@MikeY -- it is true.  I can't think of any outside references off the top of my head though.  Certainly I've seen outside references in the past and have long been aware of this topic.  One of Piggot's books on soaring from many decades ago did cover this, for one thing.

Ahhh, it just clicked...

It may be something to this, but we must remember a plane will quickly adjust to a change in "relative wind".  I have learned the long wings of a glider are very sensitive to minor changes in airflow.  What may be happening here is the change in relative wind kicks BOTH wings to a different position on the lift to drag curve, resulting in a yaw/roll that would "feel" like a change in AOA.  Great question.

@quietflyer thanks for the advice. I improved my question by edited the first paragraph so it is not misleading. I am still trying to wrap my head around your answer.

@nouveau it really boils down to how much lift you need to generate from each wing to perform the maneuver, and to do it at a safe flying speed. There is no general rule.  Your airspeed and AOA requirement (aileron settings) will also depend on how much dihedral or pendulum roll stability you need to neutralize to hold the bank.  So get with someone familiar with your plane and fly with them.

@nouveau maybe the added videos will help -- they are kind of rough; I made them made some time ago to illustrate a similar discussion on another forum

@RobertDiGiovanni the questions is really not about "required aileron settings"-- that is a whole 'nother can of worms entirely.  It's not completely unrelated, but you'd have to take many more factors into account to accurately predict the required aileron settings.

For the moment let the AOB of the aircraft be zero, assuming it is actually in a flat turn (just ruddering it's way around). Stealing this answer from Reddit, best description I have seen (my bold emphasis below), Props to grizzleeadam
https://www.reddit.com/r/flying/comments/83itwf/angles_of_attack_in_climbing_and_descending_turns/dvjdsxc?utm_source=share&utm_medium=web2x

Think of a spiral staircase with an inner handrail and outer handrail.
  Both handrails must ascend the same vertical distance, however, the
  outer rail travels a longer distance over a more sweeping path, as it
  has a larger radius. This means the inner rail is shorter, and reaches
  the same vertical height in less distance travelled - it must have a
  steeper angle.
Now try to imagine the rails as the relative wind of a climbing
  airplane. If the inner wing laid flat across the inner handrail, due
  to the steeper angle of the inner rail, the outer wing would have a
  gap at the leading edge - this translates to a higher AOA on the
  outside wing in a climbing turn.
For a descending airplane, this time the outer wing must lay flat
  against the outer rail, and the steeper slope of the inner rail would
  cause a gap at the inner leading edge - a higher AOA of the inner wing
  in a descending turn

Here's a picture, with the railings unrolled. The inside wing follows the inside rail on a steeper path. Let the wing lay flat on it. The outside wing follows the outside rail on a less steep path. The gap between the wing leading edge and the outside rail in the increase in AOA that it sees as it follows the rail in its spiral upward.

For a descent, the roles reverse, with the outside wing now having a lower AOA in the inside.
To accommodate a bank angle in understanding the problem, just shift the inside railing down.
Edit...
Another picture. This time, I have a body fixed reference frame with the X axis out the nose, the Y axis out the left wing, and Z axis up (I know, should be flipped, but just looks better this way). The body fixed frame is embedded in an inertial frame with about 45 degrees of roll (picture the left wing going out the Y axis) and a little bit of pitch up. This is an aircraft in a climbing turn. The rotation vector in the inertial frame is straight up (dashed line). This rotation must be the vector sums of rotations about the X, Y, and Z axes. The amount of those rotations is just the projection of the rotation vector onto those axes (the thick black arrows). Because the nose is pitched up, there is projection onto the X axis, therefore there is roll.

Yes that is another valid way to look at the situation.  The rails represent the direction of the local relative wind at each wingtip.  It appears we could add the bank angle into the picture simply by lowering the height of the entire inside rail by some amount.  Once we do this, the roll rate can no longer be zero.   It's interesting how the same problem can be approached in several different ways.  Is it possible that neither answer fully considers ALL the relevant effects at play?

I think that if we correctly match the bank angle to the turn rate, so we aren't skidding around, we end up w/ a situation where it is equally valid to say that the change is angle-of-attack is caused by the roll rate or by the "spiral staircase" effect-- the difference in direction of local relative wind between the two wingtips.  You can't have one without the other.

See my update on bank angle. I agree with you on the roll rate. If you take a model airplane and give it some bank and pitch, and then rotate it through a vertical axis (climbing or descending turn) you do get some roll, pitch, and yaw rate.

@Mike Y for any relative wind, the gap is either at the LEADING edge of the inside wing or the TRAILING edge of the outside wing.  Just grabbed a ruler and tried it.

@MikeY thanks for the answer. From your quotation, I still struggle to understand that "due to the steeper angle of the inner rail, the outer wing would have a gap at the leading edge - this translates to a higher AOA on the outside wing in a climbing turn." I cannot visualize what gap this is. Do you mind elaborating a bit on this? Thanks again.

Check my new picture.

". Your picture shows that the outside wing has a lower AOA because the relative wind must be the same (from any direction) "-- not so-- even if altitude is constant, in a turn different parts of the aircraft experience different relative wind directions due to rotation.  The relative wind is curved not straight.  And when roll rate is not zero, the relative wind is "twisted" as well as curved.  That's the key to understanding what is going on here.

You are right, I should have said the the wings are different paths (the rails) and have different relative wind.  Can't agree the outside wing will ever have a higher AOA, but wing tip speeds do equalize as plane progresses into the vertical as in a dive or climb.  That is where I believe the aileron inputs are creating roll.  However, I may have found another source, the assymetric canted Vstab will also create a rolling force ascending and an opposite rolling force descending.

@Mike Y +1 for your presentation.  Still think you can't believe everything you read.  Consider the spiral dive.  Pulling the el only tightens the spiral.  But thanks for your point of view.

I learned a lot from the question!

Here's one way-- not the only way-- to look at the dynamics involved--
Imagine an aircraft in a 45-degree-banked constant-altitude turn.  Now imagine that the pilot gradually adds more and more power and the aircraft gradually enters a steeper and steeper climb until it is climbing almost straight up.  Can you see how to maintain a constant bank angle, the aircraft must actually roll toward the high wingtip?  As the climb angle gets steeper, the maneuver gets closer and closer to resembling a vertical rolling climb, with the direction of roll being toward the wingtip that was originally the high wingtip in the constant-altitude turn.
"Fly" through the maneuver with your hand or with a little hand-held model airplane until you understand this.
(Like this-- https://vimeo.com/128025851#t=157s -- video intentionally starts at 2:37)
Now, can you see how a rolling motion always tends to increase the angle-of-attack of the descending wingtip, and to decrease the angle-of-attack of the rising wingtip?  As the descending wingtip comes down through the airmass, the local relative wind blows "up from below" compared to the local relative wind closer to the aircraft centerline-- this is an increase in angle-of-attack.  Similarly, as the rising wingtip moves up through the airmass, the local relative wind blows "down from above", or at least blows up from below at a shallower angle than the local relative wind closer to the aircraft centerline.  This is a decrease in angle-of-attack. These changes in angle-of-attack create an effect known as "roll damping"-- a resistance to rolling.  This is why the roll rate doesn't just keep getting faster and faster as long as we hold the ailerons in a deflected position.
So that's the answer to your question. In a constant-banked climbing turn, the aircraft is continually rolling toward the high wingtip, so the high wingtip experiences an increase in angle-of-attack and the low wingtip experiences a decrease in angle-of-attack.
Note that while our thought experiment involved a continual increase in climb angle and climb rate, the basic dynamics we're talking about are present even in a climb at constant angle and rate. In a climbing turn, an aircraft must continually roll toward the high wingtip to hold the bank angle constant.  Otherwise the bank angle will increase.  It's not a matter of aerodynamics, but rather of three-dimensional geometry.
In a descending turn, everything is the same except that to keep the bank angle constant, the direction of roll must be toward the LOW wingtip, so the low wingtip experiences an increase in angle-of-attack and the high wingtip experiences a decrease in angle-of-attack.
"Fly" through the descending turn case with your hand or a little hand-held model airplane until you understand that the extreme case of a constant-bank descending turn is a vertical rolling spiral, with the direction of roll being toward the wingtip that was originally the low wingtip when the plane was turning with a constant altitude or with a less-than-vertical dive angle.
(Like this-- https://vimeo.com/128025851#t=128s -- video intentionally starts at 2:08)
As a footnote, you can see how aerodynamic "damping" in roll -- the tendency for the roll rate to decrease-- exerts a destabilizing influence in a climbing turn, tending to make the bank angle increase.  In a descending turn, aerodynamic "damping" in roll tends to make the bank angle decrease.  This is very noticeable in some applications, such as powered hang gliders and trikes.
As another footnote, understand that we are speaking of "ascending" and "descending" relative to the surrounding airmass-- an unpowered glider spiralling up in a thermal updraft is still in a "descending" turn for the purposes of this discussion.
As yet another footnote, we can observe that it is easy to see how the bank angle can change when we pitch up with zero roll rate, in some version of a chandelle or wingover for example. It is harder to see how bank angle can be constant and roll rate can be non-zero in a climbing or diving turn, but it's true, as illustrated in the video links given above.  Again, it's fundamentally a matter of 3-dimensional geometry, not aerodynamics.
In closing, here is a link to a diagram from John S. Dencker's "See How it Flies Website" that illustrates how a rolling motion creates a difference in angle-of-attack between the two wingtips.  The diagram is not dealing specifically with the constant-bank case, and also it is really aimed at explaining "adverse yaw" which is a separate issue, but it still may be helpful-- https://www.av8n.com/how/htm/yaw.html#sec-adverse-yaw

With a descending turn, don't you actually mean a negative G turn (with the lift forces pointing downwards)? I don't see how the AoA can otherwise be higher at the low wingtip.

@hrobeers-- certainly not.  I'm sorry, I'm not understanding your point. My answer explains why the AoA is higher at the low wingtip than the high wingtip-- it's due to the non-zero roll rate, even though bank angle is constant.

@ quiet flyer-- ok I see, thanks for clarification.

@quietflyer thank you for your answer. forgive my ignorance but I think you explained it from a practical perspective but I was looking for a more theoretical answer. You seem to show that the airplane rolls one way so AOA is changing. But I thought it should be that AOA changes (for some reason I dont understand) so the airplane rolls one way?

Obviously the video would have been made slightly differently, starting with the climbing case, if it had been made specifically for this answer

I will post a follow up question as some really interesting issues are being seen here regarding adding power to a banked turn compared with level flight. Work continues...


text:
Could a hybrid electric steam plane be more efficient at altitude than at sea-level, and how to optimise it to frigid air?
In the thirties a steam powered plane was built.
video
Could a hybrid electric steam plane be more efficient at altitude than at sea-level, and how could such a steam engine be optimised to benefit from frigid air at altitude?
Perhaps there are two advantages to going hybrid.

The steam engine can be down sized to cruise power levels.
The radiator is being cooled by frigid stratospheric air < -40 deg so can be smaller.

This is a parallel hybrid, the electric motor drives the propeller until the plane is at altitude. Once at altitude the electric motor is disengaged and the small steam engine starts up and engages with the propeller.
[edit]
There is a replica of the Besler engine at the Smithsonian. It has more specs than the video. It had a condenser
Steam Car Developments
and Steam Aviation, VOL. III. JUNE, 1934 NO. 28., The Besler Steam-Driven Aeroplane
'Under the fuselage nose is the condenser, which is simply a section of an ordinary petrol car radiator, and this is said to be sufficient to recover more than ninety per cent. of the water from the exhaust steam.'
'The tests have shown that ten gallons of water is sufficient for a flight of 400 miles.'

So you have an electric engine to reach altitude, but then a different engine to cruise? I'm not sure what you are proposing, your question isn't clear.

might the radiator recover some of its drag by being placed in diverging converging duct, making a feeble subsonic ramjet.

A ramjet requires fuel @tobe. I suggest you add some diagrams or additional explanation of what you have in mind because at the moment it really isn't very clear.

I've added that the steam engine is used once at altitude. Is that clearer?

The radiator is dumping heat into the duct just through conduction not combustion? ;)

okay maybe diagrams later. Can we imagine the plane in the video. but with two added electric motors on the  wings like a trimotor.  The steam engine in the nose. The steam powered propellor is feathered till we are at altitude and the steam engine started, while the electric engines and propellors are stopped and feathered once at altitude.

Rather using steam intake what about a steam exhaust! With an hydrogen high pressure tank, and a fuel cell (in our case the hydrogen) that will generate electricity to drive electrical motors. The efficiencies of the hydrogen cell and the electrical motor is much better than direct combustion of the hydrogen. The exhaust here is just vapor (steam if you prefer)

The only reason to use steam is probably nuclear. And you are actually right, using electricity to take off and nuclear power to cruise is better than electricity only or nuclear only.

Possible? Yes. Viable? No.
A steam airplane is possible to build and fly, as a novelty hobby project. Modern technology will even allow a steam-powered airplane to have performance comparable to a very low-end homebuilt.
The term "airliner", however, implies regular passenger service for the purpose of getting from A to B. A steam-powered passenger plane is going to be completely useless for that purpose, as long as internal combustion engines exist. ICE have better efficiency, better power/weight ratio, and better reliability, sealing the deal.
The only advantage steam engines retain in the ICE era is the ability to run on solid fuel, like coal or deadwood picked up along the way. This kind of fuel produces much less power than oil and can sustain trucks hauling supplies to a besieged city, but not an aircraft that means to do more than short hops a few feet above the ground.
While the exhaust of hydrogen-powered turbines is mostly steam, so is the exhaust of kerosene-powered turbines, so both still count as gas turbines, not steam ones.
One possible modern attempt at a steam-powered airplane (not airliner) was the Tupolev Tu-95LAL, a flying lab for prototyping a nuclear-powered airplane. The Convair X-6 was another attempt that also stopped well short of any nuclear-powered operation. The only reason they'd count as steam-powered (had they actually used their reactors for power) is that steam is required to extract mechanical power out of operational nuclear reactor designs.
With liquid hydrocarbon fuel, gas turbines or at least piston ICE give you more power and more range for the same amount of weight, so steam will not return in this form. The advances in compact nuclear reactors might see more use of mobile steam power, but aircraft are more likely to go outright electric than nuclear.

I've edited it to just be a high altitude plane, not airliner, and added some links that claim the Besler plane had a condenser.

Also the Besler plane was running on a cheap and low flamabiliiy oil. The plane was very quiet.

@tobe Turbine-powered airliners are extremely quiet, considering how powerful they are. An A380 feeds on up to 200 MW of power - 1,800 times more than that old plane. You could make a steam Piper and even build a steam-powered Tu-95, but it won't be quieter than modern airliners.

Forget the electric stage - when using steam, you will most likely already have mechanical energy and when ducting that steam through a turbine, even rotational energy to turn your propellers. What advantage do you expect from converting that rotational to electrical and directly again to rotational energy?
That design could be simplified even more: Instead of heating water, the fuel could heat compressed air and let that run through a turbine. That is how any modern jet engine works.
In order to keep mass down, the steam would need to be condensed in a cooling circuit. While the wing surface could be used for this, the required piping would add a substantial weight penalty. In an open circuit where the relaxed steam is simply dumped overboard (like on the Besler biplane or most steam engines), range would be rather limited.
There was to my knowledge a single attempt at building a steam-powered airplane with steam condensation. This was a version of the Messerschmitt 264 bomber which was supposed to run on a mixture of coal powder and heavy oil instead of gasoline. It was never completed.

I've added links that claim the plane in the video had a condenser.  I think gas turbines have quite high exhaust gas temperatures.  I was wondering if a steam  engine at altitude could expand to a lower pressure and increase the temperature difference between heat source and heat sink.

or potentially the steam engine output might be condensed by a heat-exchanger that warms a second fluid like butane that drives a similar engine and the butane is then finally condensed in the radiator by the icy high altitude air.

@tobe: The linked video sure shows a steam engine without condenser. You are right about the higher efficiency at altitude, but this works the same for jets.

The articles claim it had a condenser and 90% condensation. But there is definitely some steam cominig out as it sets off! Maybe that is 10%, or a transient. I hope they weren't exaggerating the level of closure.

@tobe: If the small radiator below the engine was used for condensation, I bet my house that the 90% are a wild exaggeration. There were steam engines with recuperation - just look to what effort those had to go!

@PeterKämpf Why do you say that Jets are more efficient at altitude - my understanding was that all internal combustion engines suffered from lack of oxygen?

@MikeBrockington: That has to do with the lower entry temperature in the thermodynamic cycle. Please see here for more. They do deliver less thrust due to the lower density, but do so with even less fuel.

Fair enough - I was lead to believe that the primary reason for flying high was the lack of aero-drag, and that planes mostly flew as high as the engines would allow.

With modern materials and modelling this should certainly be possible. The efficiency is likely to be VERY low though. If I was inclined to try, I would use the steam engine to create electricity to power the electric motors that you have for take-off - that would probably save a bit of weight. On the other hand, a sterling engine would probably be a bit better again - they use air or some other gas as the working fluid, rather than having to carry water or some other heavy liquid.

yes, using the steam engine to run a generator removes a lot of complexity. not sure if a stirling engine would have the required power to weight ratio.

Not sure if there will be much of a market for a "choo choo plane".

@JohnK It’s any kid‘s dream though!

@tobe A sterling engine probably has a better chance than a steam engine - not exactly known for their high power to weight ratio!

Look at contrails. In a way we are already doing it as combustion produces water, as well as CO2.
This concept is actually very similar to a small motor charging a battery to run an electric motor (diesel-electric). There is a significant weight savings here, which partially offsets the extra weight of the battery or pressurized steam tank.  The motor only needs to produce the AVERAGE amount of power required, peak loads are handled by energy stored in the battery or steam tank.  And the music wasn't that bad either.
So efforts to make it practical would be recovery of the steam, reducing the amount of water required to operate.
But if you used pure hydrogen as fuel, it may be possible to recover water from the exhaust by condensing it, and then re-extract heat energy from the engine to make steam.
The hydrogen (or natural gas) would power conventional propulsion, with water/steam utilized for (total loss) cooling and/or extra thrust.
But weight and complexity factors would have to be considered.

I added links that claim the Besler steam plane already had a condenser. I also think it had a flash steam boiler like the more advanced steam cars of the time.

@tobe there are some very interesting readings on SOLAR powered high altitude aircraft.  Up there, weight savings is an extreme priority. I would also check with The rec about  burner/boiler efficiency vs internal combustion engine.  Not too many "steamers" around today (high pressure risks as well).  But energy storage to AVERAGE power requirement is a worthy goal, trains utilize it today.

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What limits high altitude powered paragliders other than the engine?
Due to their extremely low wing loading, powered paragliders stall at very low indicated airspeeds compared to other airplanes.  A typical paraglider can continue flying all the way down to 10-15 knots.
That suggests the idea of using a fabric wing for flight at very high altitudes.  At 100,000 feet, for example, an IAS of 10 knots corresponds to a TAS of 85 knots, well below the speed of sound.  Suppose that we take a power source that works at low air density – say, a solar-powered electric motor or an engine with an onboard oxidizer tank – and attach it to a paraglider.  Would anything prevent such an aircraft from flying stably at 100,000 ft?  For example, would flutter be an issue?

Be aware that stall speed is not constant, but increases with altitude...

Why not ask about an unpowered paraglider? It seems silly to specify that it must be powered, only to immediately dismiss the importance of a power source :)

@Sanchises Because I'm interested in reaching a high altitude starting from the ground.  If you want to fly an unpowered paraglider at 100,000 ft, wouldn't you have to launch it from something like a high altitude balloon?

@tsg Isn't the increase in stall speed mostly due to Mach number effects?  85 knots is fast, but not that fast.

Time is going to be a problem - it could take days to get up to altitude at those low speeds; oxygen, hydration & thermal support for the pilot will add weight & complexity to that of any fuel or propulsion. An extremely tough young German woman got to 33,000ft with a paraglider in 2007, but she was unconscious for a lot of the time. https://en.m.wikipedia.org/wiki/Ewa_Wi%C5%9Bnierska   https://youtu.be/TEpKNla63Kw

Related: https://perlanproject.org/ (composite wings and unpowered glider -- climbing up from low altitude though), stall speed is somewhat higher, just under 40 kts, but still subsonic at 100,000 ft and 76 thousands feet already reached. It can be good reading for information on high-altitude flight.

@tsg, a wing will stall at the critical angle of attack.  It doesn’t recognize altitude or TAS.

@tsg and indicated stall speed is constant for a given loading, which is what the OP mentioned.  Only true stall speed goes up.

Note that OP doesn't specifically mention a human pilot.

Stalling speed increases with altitude. Maximum altitude is the point at which stalling speed rises to meet maximum airspeed. To get higher, the options are to; increase thrust, increase wing area, reduce weight, or improve aerodynamic efficiency. These principles apply to all aircraft using aerodynamic lift.
In the case of the paraglider, its aerodynamic efficiency is not very good. So maximum airspeed is low and the stall speed will soon catch up with it as it climbs. It is worth sacrificing a little weight to greatly improve the wing profile and enclose the pilot and engine - but the plane is then no longer a paraglider.
The other main problem with a simple paraglider is pilot support systems. Time to altitude is measured in hours, during which time the pilot lives inside a pressure suit; the kind of thing worn by Lockheed U-2 pilots on an intercontinental reconnaissance flight. Refreshments, especially drinks, will be necessary. If you put all the support equipment in a great big backpack, like an Apollo astronaut but with longer EVA endurance, where are you going to put the engine? Something a step up from a paraglider again becomes a necessity.

The engine is an issue as you have already identified so I won't
address it here. But suffice it to say that most paramotors run on
two stroke engines and don't perform well in low oxygen air. You
also have to adjust the carburettor in flight which is often
impossible. There's a reason Gilo Cardozo took so long in designing
a new motor for his Everest flight and why he went for a rotary
engine design.
Existing paramotors are more likely to be limited by fuel capacity
(see point 2 below) than the engine though.

It depends on your definition whether this counts as engine related
at all (it's not specific to internal combustion propulsion), but
even if you ignore the lower oxygen density, fuel capacity is an
issue for altitude flights. I don't know whether you are concerned
about taking off from close to sea level or not, but even the most
efficient wing/pilot/engine combinations take a decent amount of
fuel to climb and there are obviously diminishing returns at lower
air densities.
For foot launch, there's a physical limit to the mass of fuel you
can carry. The same also applies to powered paramotor trikes but the
sub-70kg requirement often is more relevant.

Related to fuel is supply of other essentials for a pilot,
predominantly oxygen and heating. There is only so much mass of
pilot support gear that can be carried and of course there's a
balancing between climb rate and takeoff mass. There's also only so
much insulating clothing a pilot can wear and still launch a
paramotor even if you use the highest fill power down and electronic
heating. A flight above FL200 will take several hours.
You also need to be aware of sweating too much at warmer altitudes
and then your sweat freezing when higher up and in wind chill.

Aerodynamics. As @Guy Inchbald explains, stalling speed increases
with altitude. Again, there's a balancing act here between airspeed
and weight.

In many jurisdictions, above a certain altitude you're in Class A
airspace. While it's not impossible to get clearance, airspace
concerns are a limit that affects record attempts. In the US,
everything above 18,000 ft msl to FL600 is Class A and all
operations must be conducted under IFR.

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text:
What are the exact meanings of roll, pitch and yaw?
I lack some 3 dimensional understanding.
What are these angles referenced to? For example, R, P, Y all start from 0, plane is flying horizontal, then it inclines its nose by 90 degrees, moving vertical like a rocket.
Now pitch is 90 degrees, but what now determines the roll?
While moving horizontal, roll may be the angle between the normal vector of the earth's surface and the airplane's up vector.
But when pitch = 90 degrees, what is roll?
Update: Can any (yaw, pitch, roll) triple set exactly describe the attitude/orientation of an aircraft?

Regarding your update: the question about sensors doesn't have too much to do with the rest of the question, you should probably ask a new one for that. Also have look at this question: What's the minimum number of sensors for a hobby GPS waypoint following UAV?.

@Bianfable thanks for all your efforts.

@quietflyer Well, I am a total starter in the aviation area, so I probably could not express myself as I wanted. Let me try again, suppose I want to design a flight controller for an aircraft. I want to know that can I get meaningful roll,pitch,yaw values via an IMU(accelerometer+gyroscope) and determine exactly in which position is my aircraft is. I think I mix the motions and attitudes. Suppose uav takes off from the runway and all the angles are taken as 0 now. With the following order, pitch 90 deg, roll 180 deg, pitch -90 deg. All these movements resulted in a -180 deg yaw?

@quietflyer I am just too confused that should I use a tracker like that or just read the values of pitch,roll and yaw by the help of accelerometer (I have no idea how to get yaw by the way) and use them to relate a specific orientation.

@quietflyer I should probably ask another question about this, thanks for all

@muyustan I may have led you astray.  I've modified my post quite a bit.  Start with bianfable's answer, then take a look at mine for a few additional things to consider especially when thinking about how a pilot rather than an engineer would express some of these concepts.

The extreme situation (singularity) you mentioned is called the gimbal lock.

Re, "my main aim is actually to be able to define the orientation for a flying vehicle" I would either use quaternions if I wanted to represent just the orientation, or I would use a matrix representation of a rigid coordinate transformation if I wanted to represent both orientation and position. Using angles to represent 3D orientations is messy, it has singularities (google "gimbal lock"), and it's too easy to make mistakes.

@SolomonSlow thanks for your answer, it looks like I'll need to have a look at to quaternions.

What are the exact meanings of roll, pitch and yaw?

It depends somewhat on whether you are speaking from a pilot's point of view or from an engineer's point of view.  Your reference to yaw, pitch, and roll ANGLES is indicates you are looking at the situation from an engineering point of view.  A pilot would tend to think more in terms of yaw, pitch, and roll as expressing RATES of rotation, or in some cases as expressing angular (rotational) changes from the aircraft's PREVIOUS POSITION rather than from a prescribed starting reference position.  If the desire is to express the aircraft's 3-dimensional position in space relative to the plane of the ground and relative to north, a pilot would tend to speak of heading, pitch ATTITUDE, and roll ATTITUDE (or bank angle).  But read on for more.

But in the pitch = 90 degrees case I cannot easily understand how can
  I think the roll.

When the pitch attitude is 90 degrees nose-up or nose-down, the yaw attitude (heading) and roll attitude (bank angle) become undefined, from the pilot's point of view.
(I've now found that this was also pointed out in this related answer which also has some other content that pertains to your question: What is the relation between roll angle and pitch angle? : )

This describes almost every possible attitude uniquely, unless the pitch angle is +/- 90 degrees. Then roll and yaw will become
  ambiguous.

Note that if you are banked (i.e. nonzero bank attitude or roll attitude, which ever you prefer to call it), then a motion that purely involves a nose-up pitch rotation and no yaw rotation or roll rotation will also increase the bank angle, and will also change the heading. Note also that a constant-banked climbing or descending turn (i.e. nose-up or nose-down pitch attitude) at a constant pitch attitude involves a roll rotation as well as pitch and yaw rotations. So, a pitch rotation is not exactly the same as a change in pitch attitude...and a lack of roll rotation does not always imply that the bank attitude (roll attitude) is not changing-- it's all a little complicated isn't it.  Generally speaking, the rate of rotation about any given axis (pitch, yaw, or roll) is not the same as the rate of change of the pitch attitude, yaw attitude (heading), or roll attitude (bank angle), respectively.   For example an aircraft pointing straight up can YAW through 180 degrees and end up pointing straight down-- it has changed pitch attitude with no pitch rotation.

Update to the question: I wonder whether any (yaw, pitch, roll) triple
  set exactly describes the attitude/orientation of an aircraft or not.
So could you please tell me that can any orientation of a flying
  object described with a unique y,p,r triplet?

In ALMOST all cases the answer is "yes".  The exception, from the pilot's point of view, is when the nose is pointing straight up or straight down (i.e. the pitch attitude is plus or minus 90 degrees).  In that case the yaw and roll attitude (heading and bank angle) become undefined and there is no easy way to distinguish between the aircraft's belly pointing north, south, east, or west, at least from the pilot's point of view.  But read on for more on how an engineer would see the situation.
It has been noted that this can be resolved through the use of "quaternions".  To learn more about that, you should probably ask another question.
Actually there is some need for refinement here.  Taking off our "pilot's hat" and donning our engineer's "pocket protector"-- If we follow the CONVENTION given in this Wikipedia article on Euler angles https://en.wikipedia.org/wiki/Flight_dynamics_(fixed-wing_aircraft) , we note that if we START with an imaginary aircraft (this is a thought experiment, not an actual  flight maneuver) in level flight with the nose pointing north, and THEN we rotate around the yaw axis by some prescribed yaw angle, FOLLOWED by a rotation around the pitch axis by some prescribed pitch angle, FOLLOWED by a rotation around the roll axis by some prescribed roll angle, we DO end up with the aircraft's position in space fully described.  With this particular sequence of rotations, starting from wings-level flight pointing north, the angles that we've rotated about the yaw, pitch, and roll axes DO end up being exactly the same as the aircraft's heading, pitch attitude, and bank angle (roll attitude).  Following this convention, the aircraft's three dimensional position in space CAN be fully described at all times with a yaw, pitch, roll "triplet"-- even including the directions that the canopy and the belly are facing when the aircraft is pointing straight up or straight down (pitch angles of 90 or -90 degrees).  Note however that unless we arbitrarily REQUIRE the roll angle to be zero in the straight-up or straight-down cases, we notice that the straight-up and straight-down cases are not described by a UNIQUE set of yaw, pitch, and roll angles.  For example, yaw, pitch, and roll angles of 90, 90, and 0 will give the same attitude in space as angles of 0, 90, and minus 90  -- in either case the aircraft is pointing straight up with its belly pointing east and its canopy pointing west.  As another answer noted, the common thread is that in the nose straight-up or straight-down cases, the direction that the belly and canopy are pointing is tied to ( yaw angle minus roll angle)  in the nose-straight-up case and ( roll angle minus yaw angle) in the nose-straight-down case.  Therefore, any yaw-pitch-roll triplets that have a pitch angle of plus 90 degrees, and roll-minus-yaw equating to some given value, are describing the same orientation of the aircraft in space, including the direction that the canopy and belly are pointing.
For most pilots it is more intuitive to simply say that the heading and bank angle become undefined when the nose is pointing straight up or straight down, but the other method obviously has applications for defining the aircraft's attitude in space for engineering purposes.
Returning to a point already mentioned near the start of this answer-- sometimes with the words "pitch", "roll", and "yaw" it is not clear whether we are talking about a rotation rate, an attitude in space, or something else.  For general pilot-speak, it seems a good rule of thumb to assume that these words refer either to rotation rates or to angles of rotation from the aircraft's previous position, unless it is very clear from context, or from additional attached words (e.g. "pitch ATTITUDE", or "pitched up TO 20 degrees") that they are being used to mean something else such as the aircraft's attitude with respect to the outside world.  "Yaw" is the most squirrelly of the three-- we might sometimes say something like "we are going west but the nose is yawed 10 degrees right" to express a crab angle, or a sideslip angle-- i.e. the angle between the direction that the nose is pointing and something else, such as the direction of the ground track or the direction of the relative wind.  (It wouldn't be clear which is meant from the above sentence, without further context.)  It wouldn't be normal to say "the nose is yawed 40 degrees" to express a heading of 40 degrees, but in some particular contexts-- for example if we are working with "Euler angles" as described above-- a "yaw attitude" or "yaw angle" of 40 degrees could indeed be taken to mean a heading of 40 degrees.  In many cases it is much clearer to just say "heading" rather than "yaw", "yaw attitude", or "yaw angle", if that's what we mean.  Likewise for "slip angle" and "crab angle"-- both of these phrases are much clearer than any phrase involving the word "yaw".
But again, if we are using the system of Euler angles as described above for engineering purposes, then we might reasonably assume that "yaw", "pitch", and "roll" may be used to denote the corresponding Euler angles with no further elaboration.  This wouldn't be normal pilot-speak.
As noted in another answer, it appears that "Tait-Brian angles" is a more accurate, or at least more specific, name for what I have called "Euler angles" in this answer.  See the wikipedia link given above for more. Also see other answers for many well-presented, valid points.

Thanks for the answer, my main aim is actually to be able to define the orientation for a flying vehicle,  so could you please tell me that can any orientation of a flying object described with a unique y,p,r triplet?

Don't know why downwotes: perhaps TL;DR. You are generally correct, except that (90, 90, and 0) <=> (0, 90, minus 90).

thanks for your efforts, I can say that I am much more clear than the time when I asked the question. But still it is a very confusing situation.

The key thing missing in your interpretation is that the order is important. Applying the same roll, pitch and yaw angles in a different order will result in a different orientation (mathematically this is because rotation matrices do not commute).
The correct order is:

Yaw (for an airplane this is typically called the heading)
Pitch
Roll

For any given attitude, there is a unique combination of yaw, pitch and roll angles that will (if applied in this order) give you the correct attitude.
These angles are only meaningful in a given coordinate system. We typically use a system where all angles zero means you are pointing North and wings and body are parallel to the ground. Based on this starting point you would apply the given angles.

(source: Wikimedia from this Wikipedia article: Aircraft principal axes)
See also the answer to this question:
What is the relation between roll angle and pitch angle?

Let me expand a bit on your example:
We start will all angles equal to zero (level, pointing North) and pitch up 90 degrees such that our nose points straight into the sky. Yaw and roll have not changed. Now we start rolling. The roll angle would now tell us in which direction the belly of the aircraft is pointing (0 degrees means belly pointing North, 90 degrees means belly pointing West and right wing pointing North, and so on).

Comments are not for extended discussion; this conversation has been moved to chat.

"Yaw (for an airplane this is typically called the heading)" - As far I understand, yaw is not the heading, but the angle between the heading and the front-to-back axis of the aeroplane. If the plane is moving in the same direction it's pointing, then the yaw is zero. If it's sideslipping a little, that's yaw.

@ReversedEngineer No, this is called the sideslip angle, it has nothing to do with yaw!

Ah, thank you for clearing it up in my mind!

@ReversedEngineer in the context of the simulations used by aircraft manufacturers, yaw is the angle of the air-frame relative to the heading, the term 'sideslip angle' wasn't on I've heard used.  For all i know, this usage may have been limited to within the operational analysis division one company (BAE).

@PeteKirkham "yaw is the angle of the air-frame relative to the heading" That does not make any sense to me. How would you even define heading in this case? Usually, heading is the direction in which the air-frame is pointing. The sideslip angle is the angle between heading and course (the direction in which the aircraft is moving).

@Bianfable sorry, was a while ago and I was simplifying. Yaw, pitch and roll were angles of the weapons platform against the airspeed velocity vector. Angle of attack was specified for each flight surface relative to the platform centre line, so the sum of pitch + angle of attack determines the lookup angle for the lift/drag table (most of which were did not include effect of sideslip)....

...  Heading is the direction relative to the ground the aircraft is flying, so will correspond to x+y components of airspeed and wind vectors, but I don't remember anyone using wind in the sort of simulations we ran (though I'm not 100% sure whether than was 'bearing' rather than 'heading').

@Bianfable - So you're saying if there's a crosswind, the direction the nose of the aircraft is pointing is the "heading" even though it's not heading that direction but rather a bit left or right of that because of the wind? (Later) Doh! Of course it is. You set heading based on a compass. The compass doesn't know about the wind. Got it. :-)

"For any given attitude, there is a unique combination of yaw, pitch and roll angles that will (if applied in this order) give you the correct attitude." This isn't true for attitudes that are 90 degrees nose-up or nose-down. You could yaw the plane to a particular heading and then pitch up/down (so that the belly of the plane is aligned in a particular direction), pitch up and then roll so that the belly of the plane is aligned to a particular direction, or some combination of the two.

Roll, pitch, and yaw have two different meanings. They can refer to either

Euler angles, which describe the attitude (orientation) of an aircraft, or
ways that an aircraft can rotate.

Euler angles
The attitude of an aircraft can be described by three angles: heading, pitch, and bank angle (sometimes called roll angle).
The heading $\psi$ (psi, sometimes called the yaw angle) of an aircraft is, essentially, the horizontal direction that the nose is pointing. It's expressed as a number from 0 to 360, where 90 is due east, 180 is due south, 270 is due west, and 360 is due north.
You can find the heading by pointing your finger in the direction the nose is pointing, then moving your finger straight up or down until it meets the horizon. The heading is the direction your finger is pointing.
The pitch $\theta$ (theta) of an aircraft, meanwhile, is essentially the vertical direction that the nose is pointing. The "lowest" possible pitch is 90 degrees down and the "highest" possible pitch is 90 degrees up. If the nose is pointed directly at the horizon, the pitch is 0.
The pitch is simply the angle between the horizon plane and the direction the nose is pointing.
Finally, the bank angle $\phi$ (phi, sometimes called the roll angle) is slightly more complicated. The range of possible bank angle values is a full circle, going from 0, to 90 degrees right, to 180 degrees, to 90 degrees left, and back to 0. (There's no difference between "180 degrees left" and "180 degrees right.")
The bank angle is the amount that the aircraft would have to roll in order to bring the wings level, with the top side of the aircraft facing up rather than down.
The singularities
The pitch is always defined. However, if the nose is pointing straight up or down, then the aircraft no longer has a heading or bank angle as described above. There's no heading because the nose isn't pointing horizontally at all; and there's no bank angle because it's not possible to roll the aircraft such that the top side is facing up.
That said, it would make sense to say that if the nose is pointing straight up or down, then the bank angle is always 0, and the heading is

the direction that the bottom of the aircraft is facing, if the nose is pointed up, or
the direction that the top of the aircraft is facing, if the nose is pointed down.

Rotations
The words roll, pitch and yaw refer to rotations about the aircraft's various axes. They refer to rotations from the aircraft's point of view (or the pilot's point of view).
Roll is a rotation about the longitudinal axis (the direction the nose is pointing). It's controlled using the ailerons. Pushing the control stick to the right, or turning the yoke to the right, causes the aircraft to roll right.
Pitch is a rotation about the lateral axis (a line parallel to the wings). It's controlled using the elevator. Pulling back on the stick or the yoke causes the aircraft to pitch up. Note that since these are rotations from the aircraft's point of view, if you're flying upside-down and you "pitch up," you're pointing the nose towards the ground, and if you "pitch down," you're pointing it towards the sky.
Yaw is a rotation about the vertical axis (a line perpendicular to the other two axes). Despite the name, the vertical axis isn't always oriented vertically. Yaw is controlled using the rudder. Stepping on the right rudder pedal causes the aircraft to yaw right.

+1 in general, but "heading" as a name is only used by pilots. Real "aviation experts" (i.e. engineers :) do use "yaw" (yaw angle) all the time. And its range is typically ±π. (The reference is often arbitrary; in most engineering problems it doesn't matter where "North" is). / The body vertical axis, to avoid confusion you mentioned in the last paragraph, is often called the normal axis.

This is the correct answer: two different axes frames, one relative to aircraft and one relative to earth. Not to be confused!

Thanks for your answer, it helped.

@Zeus Huh, I didn't know that. All right, I've edited my answer to say it is called the yaw angle after all.

The attitude angles are explained in this wikipedia page, but it seems your confusion stems from the fact that they can present a singularity.
Each set of unique Euler angles, outside of the gimbal lock state, represent a unique attitude. In the singularity state, however:

The angles α, β and γ are uniquely determined except for the singular case that the xy and the XY planes are identical, i.e. when the z axis and the Z axis have the same or opposite directions. Indeed, if the z axis and the Z axis are the same, β = 0 and only (α + γ) is uniquely defined (not the individual values), and, similarly, if the z axis and the Z axis are opposite, β = π and only (α − γ) is uniquely defined (not the individual values). These ambiguities are known as gimbal lock in applications.

To avoid this singularity, you should use alternative representation methods, like quaternions. These are 4-dimensional vectors that nonetheless have only 3 degrees of freedom (because their modulus is normalized).
One of their main advantages is that they do not have discontinuities in their representation of the 3 dimensional attitude space, unlike the 3 dimensional representations.

Euler angles are relative to earth axes. Pitch, roll and yaw are relative to aircraft axes. Pitch means: nose up/down. Roll means: wingtip up/down. Yaw means: nose left/right. All from the pilots viewpoint. It is that simple.
As confirmed by the Wikipedia article on Euler angles:, which first mentions proper Euler angles, then Tait-Brian angles pitch/roll/yaw in the moving aircraft reference frame.
In Full Flight Simulators, the code computes:

forces and moments on the airframe in response to flight control deflection.
Linear thrust, drag, speed, vertical speed - in aircraft axes.
Angular inertia response to moments. In aircraft axes, pitch/roll/yaw, no matter what the position of the nose is.

Only then is the world position and orientation of the aircraft integrated and computed, in 6 Degrees of Freedom. This cannot be done with Euler angles, due to the nose-up singularity, and has to be done with quaternions. More on these here and here.
The term "roll" is normally used for an intrinsic motion: axes frame attached to the moving body. Roll angle starts at any convenient zero angle. The choice is pretty clear for fixed wing craft and helicopters, not so clear for a rocket. Whichever zero was chosen, after rolling 360 degrees it comes back to zero again, regardless of where the nose is pointing now.

Then pitch roll and yaw are meaningful only during a short amount of time while doing the motion. Because after the motion is ended, then according to your saying, R,P,Y are aleays 0 relative to aircraft axes. Did I get your point right? Thanks anyway

No, pitch acceleration is integrated into pitch velocity is integrated into pitch position. Zero position in pitch/roll/yaw can be arbitrarily chosen. For zero pitch and roll the earth gravity plane is chosen. Zero yaw does not have a very convenient consistent zero, north can be chosen, or position of the nose at the gate upon departure.

then by "relative to aircraft axes" you meant a fixed coordinate system not changing always during the flight. Then how does it differ from the earth axes?

"Euler angles are relative to earth axes."-- is this really always true?  For example, at https://en.m.wikipedia.org/wiki/Euler_angles, we read "Intrinsic rotations are elemental rotations that occur around the axes of a coordinate system XYZ,  Therefore, they change their orientation after each elemental rotation."   We also read "Euler angles can be defined by intrinsic rotations.  The rotated frame XYZ may be imagined to be initially aligned with xyz, before under going the three elemental rotations represented by Euler angles.

@muyustan An aircraft flying nose up still rolls: roll to the right means the right wing goes down relative to the pilots eye point, who is looking straight up.

@Koyovis I guess from a pilot's point of view, it is simpler. But from an outside view, how can you distinguish any of the 360 degrees of roll when pitch is 90 degrees? I guess it is undefined as lots of people mentioned in their answers. Also a roll motion is not something confusing but the one which is not clear is what the specific roll angle of any orientation of the body is.

@muyustan That is because you are using the term roll for an extrinsic motion, while it is meant for an intrinsic motion. Roll angle starts at any convenient zero angle - the choice of which zero position is not so clear for a rocket, but it still rolls. Whichever zero was chosen, after rolling 360 degrees it comes back to this same zero.

@Koyovis after re-reading all answers and comments, I think I get your sayings in these comments. R,P and Y are obtained by cumulative gryoscopic measurements(integrated up to position). But if an airplane starts its travel from an inclined runway lets say 15 degrees up, then will its pitch angle during the flight be 15 degrees offsetted from the horizontal level? Or is there a procedure something like maybe calculatng the take-off incline of the plane and set starting pitch angle equal to it?

One very important aspect is that roll, pitch, and yaw, relative to the aircraft (and the pilot that controls it) never change.  As you progress as a pilot, using sky/ground as your reference is usually where we all start, indeed, as land walking folks, this is how we see our world.
Practice flying model aircraft can help eliminate this mode of thought and replace it with simply using the controls to fly the plane where you want to.
"Inverted" flight becomes stick forward to the sky to keep flying.  Rolling through 360 degrees, again, roll to the sky.  Yaw (turn) to your desired compass heading or visual reference.
This is truly flying in 3 dimensions.  Roll, Pitch, and Yaw are With Respect To the Aircraft.
Gyroscopes are used to keep track of the original sky/ground reference.  Newer models have a safety switch that will "right" the plane in less than a second.  These may be worth looking into.

hey, thanks for the answer , but your language came little bit confusing to me(probably because of me not you, I am not a native speaker). Does your 2nd paragrapgh implie "I should buy a model plane and control it to get used to these values" ?

Yes, absolutely.  For a pilot.  Mathematically, it may be more breaking the position into R, P, Y vectors WRT earth/sky.  Interesting logic as a gyro displays position relative to where its original position was (starting out level).  Visual takes real time info that (hopefully) the pilot interprets (correctly).

This is a truly interesting point, it relates to the mental picture of yourself vs world. A lot of research has been done in this area. However, I'm afraid it is not directly related to the original question and will only confuse the OP.

The statement that pitch/roll/yaw is related to aircraft axes is correct.

@Zeus. Training with models gave me enormous confidence when steep bank angles were done in full scale training.  I remember instructor sharply rocking the plane back and forth and asking me "you mean, you aren't afraid of this?".

Just don't get overconfident: there are situations that are much easier to get out of with a model than with a full-scale aircraft :)

Either way, you need a reference to the ground: to navigate, to climb. You need to know how to manipulate controls to get what you want, and what you want is usually in relation to the ground. It is rather a question which of the two is your 'primary' mental reference. Some research I mentioned concludes that fighter pilots that have this mental picture of seeing yourself from the fixed world, like RC pilots, as opposed to seeing the world moving around you, are more successful. This is also related to the way attitude is presented to the pilot (the AI type problem).

Agree with the danger of overconfidence, especially stepping into a new type.  With a larger, heavier aircraft, the inputs may be correct, but you simply run out of time/altitude.


text:
Is breaking a FAR an issue when flying outside of FAA jurisdiction?
When flying outside the US it is advisable to follow the FAA rules when they are stricter than ICAO, and when it does not violate the local flight governing body's rules.
Can you still be fined or get into trouble or does the FAA only have jurisdiction in USA airspace?

Are you flying a US registered airplane?

The FAA only has Jurisdiction over US airspace and you must follow the rules of the airspace you are flying in/through. If you are talking about N registered airplanes they must follow FAA rules for airworthiness etc. even if they are kept outside the country.
Here is in interesting question on breaking laws on a plane in general (sort of applicable here)
Side Note: Although the FAA does not have jurisdiction outside US airspace if there is an accident involving a US built aircraft (mainly Boeings at this point) the NTSB will send a representative to compile their own report (and aid in the investigation). I know this happens for commercial accidents I am unaware if they send representatives for US build GA plane accidents outside the country.
Side Note 2: US pilots licenses are valid elsewhere in the world and allow you to fly elsewhere in the world certain actions elsewhere in the world (if caught/reported) may lead to the revocation of your US issued license. There is some info on that here

In international flying you are the servant of many masters.
Off the top of my head you would be answerable to:

The country in whose airspace you are flying.
If the country you're flying in requires you to walk backwards around the aircraft three times while singing Hakuna Matata prior to takeoff you best start warming up your singing voice.
In a more practical example some countries require flight plans for all flights (including VFR flights) - if you're a US pilot flying a US-registered aircraft under visual flight rules in one of those countries you would still need to file a flight plan with the appropriate authorities, even though that's not required under US regulations.
The country in which your aircraft is registered.
A US-registered aircraft is subject to US airworthiness requirements, regardless of where it is being operated. If you ignore an airworthiness directive your airworthiness certificate is invalid (and thus you likely can't operate that aircraft anywhere, as the various reciprocal agreements and treaties which would let you operate that aircraft in other countries are contingent upon the airworthiness certificate being "valid").
In addition to airworthiness requirements there may be other requirements or restrictions imposed on your aircraft by its nation or registry.
The country which issued your pilot's certificate / air carrier certificate.
A certificated entity is obligated to comply with the regulations of the agency/country issuing that certificate. So a US scheduled airline is still obligated to comply with Part 121 of the FARs, and US pilots are obligated to comply with relevant sections of Part 61 and Part 91.
For example, if you somehow find a country with no restriction on alcohol use and flying you're still bound by the 8-hour rule in 91.17 - your US (US-issued) pilot certificate could be suspended or revoked for violating that restriction, even if the country you're in doesn't care.

So in order for you flight to be legal you would need to comply with the most restrictive set of applicable laws, regulations, and guidelines.
Most aviation regulations are broadly similar (thanks to ICAO), so this is not usually a problem, but it's something you would need to be aware of prior to any flight in another country's airspace.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/3.0/


text:
What is the typical climb angle (versus the ground) of a single engine piston plane?
What are the normal climbing angles against ground on a SEP (single engine piston) plane and an airliner?
(no wing-air angles in here, but the climb angle when watched from the side of the plane)

(Source: user11961 - Own Work)

There is no "normal" angle: it's different for different types of airplane, and even for one airplane it depends on the desired rate of climb.

Okay i see that is true. Then what is like a "normal typical average" climb angle for an airliner? 10-15degrees maybe?

Between 0 and 20 degrees, anything goes. This depends on desired rate of climb, center of gravity, take-off weight/mass, FLEX settings, pilot mood and the how Jupiter is aligned to Venus.... too many factors. ;)

@Simon :D - credit where credit's due...

+1 for incredibly crudely hand-drawn airplane! Makes the non-artist in me giggle with glee.

That depends on wind speed and the aircraft's thrust-to-weight ratio.
Here are some values, all valid for sea level

GA aircraft: 4 m/s climb speed, 36 m/s airspeed. In calm air, this becomes a climb angle of 6.3°. If the wind blows with 36 m/s, the aircraft will climb vertically relative to earth if it flies straight into the wind.
Airliner: 20 m/s climb speed, 120 m/s. In calm air this becomes a climb angle of 9.5°.
Empty airliner: 30 m/s at 100 m/s. In calm air this becomes a climb angle of 16.7°. At airshows this is used to dramatic effect.

Note that the spectacular angles at airshows involve the conversion of airspeed to altitude, so these maneuvers are instationary.
If you want to know more on computing the optimum climb angle, consider reading this answer.
The main influence on climb speed is the thrust-to-weight ratio of the airplane. Since thrust depends on flight speed, ambient temperature and air density, those factors control the attainable climb speed in combination with the aircraft's weight.
For an observer, the next important influence is wind speed, since the aircraft climbs relative to the air mass it is flying through. If this air mass makes the aircraft appear to fly more slowly, a steeper climb angle can be observed.

Climb performance over airspeed and thrust-to-weight ratio for an idealized turbofan engine. The blue lines show thrust (right Y-axis) and the green lines the resulting climb speed. The two black lines show how the optimum flight speed for best climb speed and best climb angle (steepest climb) vary over thrust loadings. They are easy to find graphically: Just measure the angle of a line from the origin to the point on a green line at the desired flight speed and the right thrust loading (thrust-to-weight ratio). If the scales of the two speeds on the X- and Y-axis would be the same, you could directly take the angle from the plot.
With lots of excess thrust, the optimum is limited by the stall speed (the black line bends into a vertical trend), while with no excess thrust both optimum speeds vx and vy converge. This makes sense: If thrust is just sufficient to keep the airplane from descending at one speed, this speed will both give the best flight path angle and the best vertical speed (unfortunately, both will be 0 at this point). It also helps to reduce induced drag, so aircraft with a high aspect ratio wing will climb steepest at a higher lift coefficient (= lower speed).

The climb angle depends on a number of factors like the airspeed, desired rate of climb, ToW, T/W ratio, airfield location (density altitude) etc.
For most commercial airliners, the typical climb angles are in the range of 15-20$^{\circ}$, while a few aircraft exceed these limits. (Added in response to @Jon Story's Comment)
The following figure shows the potential climb angles of Boeing airliners:

Image from Boeing AERO magazine
Note  that the actual values will be different depending on various conditions as already noted.
As for GA aircraft, the typical climb angles will be in the range of 5-6$^{\circ}$ at sea level and decreasing with altitude, with other conditions being equal.

Although the chart is nice, a quick description would be nice for searchability/readability: something like this, placed above or below the "As for GA aircraft" section: "For most commercial airliners, roughly 5-10 degrees on takeoff and around 15-20 degrees on climbout would be typical, with a few specific aircraft being closer to 10 or 25 degrees."

@JonStory just make that the description for the image ;)

It can be the description, but I meant for people as well as accessibility - the image is good but requires some deciphering while a simple sentence could do the same job

all_licenses: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/3.0/


text:
Why, after decades of redesign and enhancement, does it still rain inside B737?
For as long as I can remember, seats 1A/1B suffer from rain during acceleration/takeoff as the condensation pours down from the heavens, (well, the overhead panel where the reading lights, gaspers, etc. are).  I guess it was, at most, a minor inconvenience until pax started carrying more consumer electronics in their hands. Now it can be costly.
Obviously, I can fix the issue myself by avoiding those seats, but sometimes they're the only extra-legroom seats left, and I'm tall. I try to remember to keep my electronics pocketed until after takeoff, but it's so boring sitting there while 188 other pax try to stuff their inflated bags into straining lockers, and I forget.
I can understand that this rotation rain, or similar aggravation, might happen on a new aircraft design; something undetected until mass operations and not safety-critical anyway, but how is this still happening on an aircraft that first flew decades ago and has had so many enhancements?  I can't be the only one who has had a Seattle soaking, so why has this, possibly costly, annoyance not been fixed?  It can't be that difficult/expensive to cure, surely?

I've never heard of this on a 737. The last rows in a DC-9/MD-80 series is where I seen this the most.
The simplest solution is for the flight crew to set the cabin temperature control to not be full cold on a humid day. Just a little heat will cut down on the condensation being developed while sitting at the gate.
Here's an interesting article on moisture in the airplane, though it is not specific to the gasper vent rain.
http://www.boeing.com/commercial/aeromagazine/aero_05/m/m01/index.html
Some larger aircraft have dehumidifiers, but as the Boeing article states

Dehumidification systems (ground-based or onboard) are effective at removing moisture but are not cost effective.

Orite, thanks.  Seems like a more common problem than I thought:(

Suffered this on a 777 from London to Dallas - definitely not an issue isolated to the 737.


text:
What is a whip stall?
I was reading 14 CFR 23.3, which discusses airplane categories. In normal and commuter categories, stalls (except whip stalls) are allowed. The regulation, however does not define "whip stalls." What is meant by this term?

It happens very quickly. "Whip", then the aircraft stalls.

The clearest definition I could find is from an AOPA quiz (of all places):

The airplane is pitched up into a vertical or near-vertical climb. It
  then pauses, slips downward momentarily (tail first), and then whips
  into a steep, nose-down attitude.

The tail-first slip backwards seems to be the defining characteristic of a whip stall. Interestingly, Whip Stall and Tumble Awareness is included in the FAA's Powered Parachute and Weight Shift Control PTS, but they aren't defined there either.


text:
Is implementation of CPDLC mandated by EASA?
Is CPDLC (Controller–pilot data link communications) mandatory by EASA? I have not heard any update that Airlines are using CPDLC. While talking to some of the pilots I heard that they have been instructed to switch the System due to satellite cost. What is the real scenario?

Possible duplicate: Which airplanes are exempt from Europe's 2015 CPDLC (Link 2000+) requirement?.  While the subject doesn't look like an exact duplicate, it does address this question as well.

A better duplicate: What additional aircraft equipment is required to fly a US registered airplane in Europe?

according to eurocontrol, http://www.eurocontrol.int/services/link-2000-programme:

The LINK 2000+ Programme started in 2001 and is now in the full scale
  implementation phase governed by the DLS IR which requires:
• All newly delivered aircraft operating above FL285 to be equipped as
  of 2011,
• Core European ANSPs to be operational by 7 February  2013,
• The rest of European ANSPs to be operational by 5 February 2015,
• All existing aircraft operating above FL295 to be retroffited by 5
  Feb 2015 (unless exempt).

What aircraft are exempt? See page 4 of this pdf: http://ec.europa.eu/transport/modes/air/single_european_sky/doc/implementing_rules/2014_01_22_2nd_exemption_under_29_2009.pdf


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How much thrust was provided by a typical Meredith Effect radiator?
The Meredith Effect was used on some aircraft to provide more thrust by channeling air through the radiator such that the air is expanded, heated and then compressed through a constriction, generating thrust.  How much thrust could such an installment generate?  How much net thrust, after accounting for drag, does such an installation generate?

the thrust contribution depends a lot on speed. At Mach 0.7 it provides thrust, at Mach 0.3 it causes drag.

@PeterKämpf could it be that the propeller is actually acting as sort of a compressor, and the (piston) engine as a heat source to create a crude jet thrust mechanism?  Or is ram effect enough at higher speeds?  I have read there is actually lower pressure behind pro hubs, but could that have been changed to help cool the engine?

@RobertDiGiovanni The pressure increase of the propeller disk is very short-lived and instantly converted into speed. Only in a shrouded prop would a pressure increase be possible. The radiator intake indeed uses ram pressure (and there you have a duct coming behind, so the pressure can be maintained. The radiator acts as a throttle, so the exit is semi-blocked. Then the pressurized air is heated and free to escape, so it picks up speed to maintain mass flow at an expanded volume).

Well, the shroud would be the engine cowling.  It would be a great study to see on what scale and speed it would have to be to make it practical.  Dedicated radiator fans are actually common in automobiles.

Here they give a calculation for the thrust generated by a Meredith effect cooler. They do this for the P51 Mustang. It is also mentioned that in Aeroplane Monthly, May 1999 (not accessible to me), the designer Atwood claims that the Meredith effects cooler generates 300 lbs (~1334N) of force.
They perform some calculations based on geometry obtained from  Gruenhagen's "Mustang. The story of the P51 fighter", 1969. These calculations also lead to a number around 300 lbs (it calculates 270 lbs of thrust).
However, the calculations do not include the effects of the heating of the air whilst passing through the cooler (which is -according to me- a vital component of how these coolers generate thrust).


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What is a rudder or fin stall?
What is a rudder or fin stall, how will the aircraft behave in that situation, and how should the pilot recognise it? What is the recovery procedure? And what is rudder reversal?

Right side slip from left rudder, rudder stalls, what happens?
This is comparable to a wing stalling in that it is caused by the rudder/vertical stabilizer
exceeding a critical angle of attack.  There for, it has passed its maximum deflection potential.  The result will be the fuselage slip will reduce until the rudder/vertical stabilizer assembly unstalls.  Just like with the wing and elevator, reducing rudder deflection will also unstall it.
Notice designers have learned 3 techniques to help prevent this:  1.  Lower aspect ratio vertical stabilizer. Just like wings, these stall at higher AOA.  2.  Swept or delta shaped leading edge.  Many 1940s era Vstabs were fantasticly ahead of their time had their planforms been made into wings.  These shapes will stall at higher AOA, allowing greater rudder deflection.  3. The all moving rudder.  Making the entire assembly a rudder (as on the SR-71 Blackbird) and making them large enough will help over come the directional stabilizing effect of the rear fuselage when turning.
Rudder stalling would most likely involve some fairly aggressive control application, which may exceed the structural strength of the vertical stabilizer.  Beyond fighters, there may not be much benefit in that type of manuever.

When the side slip is high, fin/rudder stall can happen. This is similar to stall of wing, but in a different plane i.e. for vertical stabilizer. When angle of attack (for vertical fin it is called side slip or Beta) of the vertical stabilizer is high in terms of relative airflow, the lift characteristics of vertical stabilizer can also behave same as wing at high angle of attack. Beyond a certain angle, airflow separation takes place and vertical stabilizer may not generate requisite force ( similar to lift for wing) and ultimately vertical stabilizer would stall.
Aircraft’s directional stability in general would be lost in this condition. How aircraft would do so, would be too particular to aircraft depending on its specific properties like inertial and aerodynamic characteristics etc.
Pilot would recognize by preemptive high side slip angles if he has indication for the same in the cockpit. Excessive Side-forces may be felt by the pilot.
How to recover ? Exactly don’t know but an educated guess, reduce side slip angles by turning into wind, may be using ailerons, there by get out of stall... guesswork, please correct me if Iam wrong.
A large rudder deflection input in one direction followed immediately by a rudder deflection input in the opposite direction is called rudder reversal.

Related: aircraft designers can prevent (or at least postpone) this by adding vortex generators upstream of control surfaces. As the name suggest, these generate vortices, which better 'stick' to the surface. You can see that for example on the Boeing 727.

I was also kinda hoping to get an answer in what direction would the aircraft turn if stall occurs on vertical stabiliser. Lets say we are in a right sideslip (by giving left rudder), if the rudder stalls, would the aircraft start to rotate anti-clockwise and perhaps then even enter a spin or it would turn in a clockwise direction and basically stabilise itself?

That depends on the stability characteristics of the aircraft. Most aircraft are designed to be stable, but especially newer generation fighter jets might be designed unstable, as that makes them more agile. These craft need their flight computers to maintain stable flight.
The principle is the same as with regular wing stall: if a wing stalls, most aircraft will descend nose down, reducing the angle of attack and allowing the wing to pick up lift again.

This answer could be improved by noting that there is are two other meanings to "rudder reversal" which may be more suited to the context of this answer-- although, granted, a series of reversing rudder inputs sometimes does in fact allow the pilot to work with the aircraft's yaw rotational inertia and "pump up" a yaw oscillation that eventually reaches a larger slip angle than the pilot could achieve  by simply deflecting the rudder and holding it.  (Think of a kid on a swing "pumping up" a large motion, versus simply moving their legs to full-deflected and holding them there.)   (Ctd)

(Ctd) So this could in fact contribute to tail stall.  Anyway, the other two other meanings are 1) malfunction of the control system, typically due to failure of a hydraulic component, that moves the rudder in the wrong direction in relation to the deflection of the pedals.  (You'll see lots of hits for this on google in relation to Bng 737.)   And 2), if you are in a left-rudder sideslip (ball to right, yaw string to left) but you are having to hold pressure on the right rudder pedal to stop the rudder from moving FUTHER left, you might call this "rudder reversal" as well.  This can be (ctd)

(Ctd) This can be caused by the fact that you are also holding lots of right aileron to overpower dihedral and stop the aircraft from rolling downwind, i.e. stop the aircraft from rolling left, and the deflected ailerons are creating a strong adverse yaw torque toward the left.  So really the ailerons are driving the slip, not the rudder.  The rudder is just "going along for the ride" and freely floating, or is actually being used by the pilot to stop the slip angle from increasing, rather than to drive the slip. (ctd)

(Ctd) If you progressively increase the slip angle still more, eventually the rudder will be locked at full-left deflection and then at that point you can relax your pressure on the right rudder pedal if you are happy to continue that slipping at that angle.  This situation is not uncommon in sailplanes.  Or in a much-worse-case scenario you may be fighting for control of the aircraft.  To read more about this sort of thing see the related answer https://aviation.stackexchange.com/a/51222/34686


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Do winglets really improve efficiency and reduce drag?
Below are some pictures of various fixed wing aircraft with winglets. It is widely accepted that these winglets will improve an airplane's performance by reducing drag and therefore improving fuel efficiency.
Here is an official video from Boeing showing the folding wing of B777x. According to Wikipedia, the wing's ratio increases from 9:1 to 10:1 which, in turn will improve efficiency up to 7%.
Here is also an official video of Boeing 737 Max that is being tested in Boeing's trans-sonic wind tunnel. In the video, it is claimed that the addition of the split winglet will reduce drag and improve fuel efficiency.
Airbus also said the claimed the same in regards to their A380. It has a claimed 4% efficiency improvement from the addition of a winglet.
But now, Boeing is developing a new airplane which with "foldable" wing, the 777x. The wing is "foldable" to accommodate taxiway width limitation of some airports. Clearly, it is not because of aerodynamics. But at the same time, Boeing claims that it will improve efficiency up to 7%.
Then my question is, if using a traditional winglet will increase the  aerodynamic as well as fuel efficiency, why does Boeing not implement this for the B777x?

Picture 1: Boeing 777x with folded wings.
Picture 2: Boeing 777x with straight wing.
Picture 3: Boeing 737 Max with Y-shape winglet.
Picture 4: Boeing 747-400 with bent-up winglet.
Picture 5: Airbus A380 with Y-shape winglet (like Boeing 737 Max).

This question and answer from Peter Kämpf may potentially be your answer: https://aviation.stackexchange.com/questions/8556/is-a-winglet-better-than-an-equal-span-extension

"Clearly, it is not because of aerodynamics" – what makes you think so? Of course the wider span improves aerodynamic efficiency.

@PeterKämpf, sorry for my unclear sentence. But to fold the wing is not due to the aerodynamic reason, but due to possibility the airport is not wide enough. Mean, it is not mandatory to fold the wing, or if possible, the wing must be extended so it can take off shorter and landing slower. Just after takeoff, the wing is extended or just before landing the wing is folded, if necessary. But the answer in your question have a good explanation.

Can we just auto-close questions with "really" in the title?

The wing is never folded or unfolded in the air! This is only possible on the ground, before take-off or after landing.

Yes @PeterKämpf, you are correct, I was wrong. There is explanation here in 3:25. BUt however, it is not official video and explanation. Sorry for the mistake and thank you for have corrected my mistake.

@PeterKämpf, but then, if it is not due to airport runway's limitation, then what it need to accommodate?

@AirCraftLover: It's about the taxiways and mostly the width of the terminal parking positions. On a 98 ft runway with lots of clearance left and right there is no reason not to unfold the wings. Span brings most benefits at low speed.

Thank you for the nice info.